Remove noise using linear regression against a DesignMatrix.
Given a column vector of data \(\y\)
and a design matrix of regressors \(X\),
we will find the vector of coefficients \(\w\)
We will assume that the model fits the data within Gaussian uncertainties:
We make the regression robust by placing Gaussian priors on \(\w\):
We can then find the maximum likelihood solution of the posterior
distribution \(p(\w | \y) \propto p(\y | \w) p(\w)\) by solving
the matrix equation:
Where \(\covw\) is the covariance matrix of the coefficients:
The light curve that needs to be corrected.
The constructor shall:
* accept all data required to run the correction (e.g. light curves,
target pixel files, engineering data).
* instantiate the original_lc property.
Measures the degree of over-fitting in the correction.
Measures the degree of under-fitting the correction.
Find the best fit correction for the light curve.
Returns diagnostic plots to assess the most recent call to correct().
Returns a diagnostic plot visualizing how the best-fit coefficients compare against the priors.
Shorthand for self.design_matrix_collection.